Why a radial pattern and not a grid?

Because the distance between the mics needs to be 1) large and 2) consistent. It would work with a grid but the mics near the middle would be "underutilized" (not maximally taken advantage of), and also in a grid the mathematics is horrendous, but with a circle it's simple.

(OP here) Primary reason is that you can make a big array with only 2 boards, a small board in the middle and a bunch of long boards around it.

Radial pattern of linear arrays with exponential spacing should also be pretty close to optimal for the distribution of pairwise microphone distances to maximize the gain with a fixed number of microphones.